1. Technical Field
The present disclosure relates to a method for detecting and isolating parametric faults in a physical system and a computer-implemented method therefore.
2. Description of Related Art
The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention.
Whatever the application realm of interest may be, a fault remains an unwelcome event causing an undesirable perturbation in the normal operation of a system, with multifarious adverse effects such as loss in efficiency, productivity, reliability and profitability for several industries. Its detection and isolation therefore become imperative measures to be taken by any industry aspiring for economic survivability and ultimate success in today's highly competitive economic climate. For these, and possibly other reasons, fault detection and isolation has continued unabatedly to enjoy an increasing importance in many crucial areas such as mission critical systems, including aircraft and spacecraft, process control industries, power utilities, gas, oil and water distribution systems. The diagnosis of faults is vital from the points of view of asset management, shutdowns reduction, condition-based monitoring, product quality improvement, process reliability, economy, safety, pollution, and conservation of scarce resources that contributes to the protection of the environment.
Fault diagnosis of physical systems is still a challenging problem and continues to be a subject of intense research both in industry and in academia in view of the stringent and conflicting requirements in practice for a high probability of correct detection and isolation, a low false alarm probability, and a timely decision on the fault status (see for example: R. Doraiswami, L. Cheded, K. M. Haris, Sequential Integration Approach to Fault Diagnosis With Applications: Model-Free and Model-Based Approaches, VDM Verlag Dr. Muller Aktiengesselschaft and Co., 2010; S. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Springer-Verlag, 2008; R. Doraiswami, C. P. Diduch, J. Tang, A new diagnostic model for identifying parameter faults, IEEE Transactions on Control Systems Technology 18 (3), (2010), pp. 533-544; M. Ferrente, B. Brunone, Pipe system diagnosis and leakage detection by unsteady-static tests, Chongking, China, in: Proceedings of the 7th International Conference on Intelligent Control and Automation, 2008; N. Orani, A. Pisano, E. Usai, Fault diagnosis for the vertical three-tank system via high-order sliding-mode observation, Journal of Franklin Institute 347 (2010), pp. 923-939; G. Heredia, A. Ollero, M. Bejar, R. Mahtani, Sensor and actuator fault detection in small autonomous helicopters, Mechatronics 18 (2) (2008)9, pp. 0-99; S. Silvio, C. Fantuzzi, R. J. Patton, Model-Based diagnosis using identification techniques, Advance sin Industrial Control, Springer-Varlag, 2003; R. Isermann, Fault diagnosis Systems from Fault Dection to Fault Tolerance, Springer-Verlag, 2006; R. J. Patton, P. M. Frank, R. N. Clark, Issues in Fault Diagnosis for Dynamic Systems, Springer-Varlag, 2000; A. Widodo, B. Yang, Support vector machine in machine condition monitoring and fault diagnosis, Mechanical Systems and Signal Processing 21 (2007) 2560-2574; R. Naresh, V. Sharma, M. Vashisth, An integrated neural fuzzy approach for fault diagnosis of transformers, IEEE Transactions on Power Delivery 23 (4) (2008) 2017-2024; M. Witczak, Advances in model-based fault diagnosis with evolutionary algorithms and neural networks, International Journal of Applied Mathematics and Computer Science 16 (1) (2006) 85-89; Bo, X. Quio, G. Zhang, Y. Bai, Zhang, An integrated independent component analysis and support vector machine for industry distillation monitoring, Journal of Process Control 20 (2010) 1133-1140; R. Doraiswami, Atwo-stage identification with application to control, feature extraction, and spectral estimation in: IEEE Proceedings: Control Theory and Applications, vol. 152 (4), 2005, pp. 379-386; J. F. Gertler, Fault Detection and Diagnosis in Engineering Systems, Marcel-Dekker Inc., 1998; M. Shahab, R. Doraiswami, An ovel two-stage identification of unstable systems, in: Proceedings of the Seventh International Conference on control and Automation (ICCA2010), Christ Church, New Zealand, 2009—each of which is incorporated herein by reference in its entirety).
In general, there are two broad classes to fault diagnosis: model-free and model-based ones.
Model-free approach: This approach includes tools based on limits checking, plausibility analysis, neural networks (ANN), fuzzy logic (FL), principal component analysis (PCA), Partial Least Squares (PLS) and more recently support vector machines (SVM). A model-free approach is capable of detecting a possible fault quickly, unraveling its root cause(s) and isolating it. Its independence from a model imparts to it an attractive freedom from the usual model-related difficulties such as identifying the required model, dealing with the presence of nonlinearities and structural complexities. However, these advantages are realized at a cost that could have various facets depending on the tool used. For neural networks, there is a lack of transparency, a need for a sufficient amount of training data covering most, if not all, operational scenarios, and a possibly lengthy training time. Fuzzy logic techniques, though less opaque than neural networks, suffer from the difficulty of deriving precise rules that distill an expert's knowledge of the application domain and which are necessary to drive the fuzzy inference engine.
Model-based approach: On the other hand, given the availability of an appropriate model, the model-based method is transparent and provides a complete and accurate diagnostic picture by exploiting a wealth of readily available and powerful analysis and design tools. Fortunately, the well-known difficulties in identifying a system model, due to its structural complexities and nonlinearities that may render its mathematical analysis intractable and its processing slow, may, for a vast number of practical systems, be mitigated by resorting to simple linearized models that are quite adequate in capturing most of the system dynamics of interest and whose predictive and inferential power can be enhanced by a rich repertoire of powerful linear analytical tools. The basic idea behind the model-based approach for fault diagnosis is to generate a signal termed the residual which, in the ideal case, is zero when there is no fault and non-zero otherwise. The ideal case refers to the situation where the model of the system is precisely known and there are no disturbances or measurement noise affecting the system. In practice however, the system is hardly free from such disturbances or measurement noise and these are either partially or totally unknown, thus making the derived model at best an approximation of the real system. There are various approaches to the generation of residuals including Kalman filter or observer-based approaches, parameter estimation methods, and parity vector methods (see for example: J. Chen, R. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, 1999; R. Doraiswami, L. Cheded, Kalman filter for fault detection: an internal model approach, IET Control Theory and Applications 6 (5) (2012), pp. 1-11-ech incorporated herein by reference in its entirety).
There are two types of fault models employed, namely additive and parametric (or multiplicative) types. In the additive type, a fault is modeled as an additive exogenous input to the system whereas in the parametric type, a fault is modeled as a change in the coefficients of the numerator and the denominator of the system transfer function or physical parameters which completely characterize the fault behavior of the subsystems. The Kalman filter is most widely and successfully used for additive fault detection while for parametric (multiplicative) faults, model identification-based schemes are employed.
The model-free approach is also capable of providing a quick visual detection of the onset of any fault from the changes in the fault signatures such as settling time, steady-state sensor output values, and the coherence spectrum of the residuals. The model-based approach has the ability for capturing any faults, especially incipient ones, which may escape capture by the model-free schemes such as neural network or fuzzy logic due to insufficient training data or incomplete fuzzy rules.
In the present disclosure, the Kalman filter residual is employed for both fault detection and isolation since (a) the Kalman filter residual is zero in the statistical sense if and only if there is no fault, and (b) its performance is robust to plant and measurement noise affecting the system output.